research-article

Product Algebras for Galerkin Discretisations of Boundary Integral Operators and their Applications

Authors:

Matthew W. Scroggs,

Wojciech ŚmigajAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 46, Issue 1

Article No.: 4, Pages 1 - 22

https://doi.org/10.1145/3368618

Published: 20 March 2020 Publication History

Abstract

Operator products occur naturally in a range of regularised boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp, we have implemented a complete operator algebra that depends on knowledge of the domain, range, and test space. The aim was to develop a way of working with Galerkin operators in boundary element software that is as close to working with the strong form on paper as possible, while hiding the complexities of Galerkin discretisations. In this article, we demonstrate the implementation of this operator algebra and show, using various Laplace and Helmholtz example problems, how it significantly simplifies the definition and solution of a wide range of typical boundary integral equation problems.

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Cited By

van’t Wout E(2024)The boundary element method for acoustic transmission with nonconforming gridsJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115838(115838)Online publication date: Feb-2024
https://doi.org/10.1016/j.cam.2024.115838
Jerez Boudesseul Rvan 't Wout E(2023)Modeling frequency shifts of collective bubble resonances with the boundary element methodThe Journal of the Acoustical Society of America10.1121/10.0017650153:3(1898-1911)Online publication date: 21-Mar-2023
https://doi.org/10.1121/10.0017650
Fierro-Piccardo IBetcke T(2023)An OSRC Preconditioner for the EFIEIEEE Transactions on Antennas and Propagation10.1109/TAP.2023.323676271:4(3408-3417)Online publication date: Apr-2023
https://doi.org/10.1109/TAP.2023.3236762
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Index Terms

Product Algebras for Galerkin Discretisations of Boundary Integral Operators and their Applications
1. Mathematics of computing
  1. Mathematical analysis
    1. Integral equations
    2. Numerical analysis
      1. Discretization
  2. Mathematical software
    1. Solvers

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Information & Contributors

Information

Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 46, Issue 1

March 2020

214 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3387915

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 March 2020

Accepted: 01 October 2019

Revised: 01 June 2019

Received: 01 June 2018

Published in TOMS Volume 46, Issue 1

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Cited By

van’t Wout E(2024)The boundary element method for acoustic transmission with nonconforming gridsJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115838(115838)Online publication date: Feb-2024
https://doi.org/10.1016/j.cam.2024.115838
Jerez Boudesseul Rvan 't Wout E(2023)Modeling frequency shifts of collective bubble resonances with the boundary element methodThe Journal of the Acoustical Society of America10.1121/10.0017650153:3(1898-1911)Online publication date: 21-Mar-2023
https://doi.org/10.1121/10.0017650
Fierro-Piccardo IBetcke T(2023)An OSRC Preconditioner for the EFIEIEEE Transactions on Antennas and Propagation10.1109/TAP.2023.323676271:4(3408-3417)Online publication date: Apr-2023
https://doi.org/10.1109/TAP.2023.3236762
Betcke TBurman EScroggs M(2022)Boundary Element Methods for Helmholtz Problems With Weakly Imposed Boundary ConditionsSIAM Journal on Scientific Computing10.1137/20M133480244:5(A2895-A2917)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1137/20M1334802
van 't Wout EHaqshenas SGélat PBetcke TSaffari N(2022)Frequency-robust preconditioning of boundary integral equations for acoustic transmissionJournal of Computational Physics10.1016/j.jcp.2022.111229462(111229)Online publication date: Aug-2022
https://doi.org/10.1016/j.jcp.2022.111229
van 't Wout E(2022)Stable and efficient FEM-BEM coupling with OSRC regularisation for acoustic wave transmissionJournal of Computational Physics10.1016/j.jcp.2021.110867450:COnline publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110867
van 't Wout EHaqshenas SGélat PBetcke TSaffari N(2022)Boundary integral formulations for acoustic modelling of high-contrast mediaComputers & Mathematics with Applications10.1016/j.camwa.2021.11.021105:C(136-149)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1016/j.camwa.2021.11.021
Cardoso Soares MBrandão Carneiro EAizik Tenenbaum RMareze P(2022)Low-frequency room acoustical simulation of a small room with BEM and complex-valued surface impedancesApplied Acoustics10.1016/j.apacoust.2021.108570188(108570)Online publication date: Jan-2022
https://doi.org/10.1016/j.apacoust.2021.108570
Search SCooper Cvan't Wout E(2022) Towards optimal boundary integral formulations of the Poisson–Boltzmann equation for molecular electrostatics Journal of Computational Chemistry10.1002/jcc.2682543:10(674-691)Online publication date: 24-Feb-2022
https://doi.org/10.1002/jcc.26825
Betcke TScroggs M(2021)Bempp-cl: A fast Python based just-in-time compiling boundary element library.Journal of Open Source Software10.21105/joss.028796:59(2879)Online publication date: Mar-2021
https://doi.org/10.21105/joss.02879
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